The city is dying for a few good cyclists — but handbag owners need not apply.

A Nightingale-Bamford School executive was pulled over by a cop while cycling on Columbus Avenue and slapped with a ticket for — of all things — pedaling with a tote bag strapped to her handlebars.

Claire Lecomte du Nouy, 38, the dean of students at the exclusive prep academy on East 92nd Street, said at first she thought the cop was just yanking her chain.

Having ridden a bike for five years in New York, Lecomte du Nouy said she couldn’t understand how the city — which is supposedly trying to encourage cycling — would hit bike riders with frivolous tickets.

“He said, ‘Could you get off your bike please?’ ” she told The Post.

“I said, ‘Why?’ He said, ‘You’re not allowed to carry a purse on your handlebars.’ I thought he was joking.”

Lecomte du Nouy, who had been riding down Columbus Avenue at West 100th Street on Monday at 3 p.m. en route to pick up her 4-year-old daughter at nursery school, said she nearly lost her balance when the cop asked for her driver’s license.

“He gets out his little notepad and starts writing things down,” she said. “Then I realized he’s writing a ticket. I still thought it was a joke.”

When she protested, she said the officer comforted her by adding, “Don’t worry, you can go to court. The judges always throw these out.”

And it turns out, that’s exactly what will happen.

The summons listed her offense as “carry articles on bicycle,” but it was only after she returned home Monday evening and did a little research that she learned the city has no such zero-tote policy.

“Not a single person knows about this thing,” she said.

Police brass — who are currently pushing a widespread crackdown on unlawful cyclists — say the summons should have never been issued.

“A summons may be issued . . . if a cyclist is transporting a bundle or package in such a way that it prevents him/her from keeping at least one hand on the handlebar,” NYPD spokesman Paul Browne admitted. Lecomte du Nouy had both hands on the bars.

“I’m really angry. I was angry at the time,” Lecomte du Nouy said.

She has 15 days to answer the summons and says she fully intends to fight it.

In the meantime, she’s now so paranoid about getting pulled over while pedaling that she keeps her eyes extra “peeled” for police and has traded her tote for a backpack.